Universal health care helps startups.
You just need it to become the norm for employers not to provide healthcare insurance.
So for example (and I am NOT saying we should actually do this) if they would simply pass a law forbidding employers from including health coverage as part of their compensation packages, then everyone would be buying their own insurance (on exchanges or wherever) and startups along with every other business would be relieved of the burden.
Before the ACA removed restrictions of pre-existing conditions, merely switching employers carried the risk of losing access to necessary healthcare.